Energy on this world and elsewhere

Instructor: Gordon D. Cates Office: Physics 106a, Phone: (434) 924-4792

email: cates@virginia.edu

Course web site available at www.phys.virginia.edu, click on classes and find Physics 1110.

or at http://people.virginia.edu/~gdc4k/phys111/spring17/home.html

February 14, 2017Lecture #7

Announcements

• Please purchase Beyond Smoke and Mirrors by Burt Richter, 2nd addition.

• New date for quiz: February 21. • Version 1.0 of review sheet will be available

later today (Tuesday the 14th). • Review sessions Thursday, the 16th and Monday

the 20th. • Reading for quiz:

- Chapters 1-3 of the class notes. - Chapters 1-3 and 5 of Feynman’s book. - Isaac Asimov’s short story, “The Last Question”.

Heat engines and the second law of thermodynamics....

Bear with me here!

First we return to the question of a heat engine’s efficiency

Hot reservoir, TH

Cold reservoir, TC

QH

QC

workefficiency = W

QH

The conservation of energy applied to the heat engine

Hot reservoir, TH

Cold reservoir, TC

QH

QC

work

Looking at the flow of energy as illustrated in the diagram at right, we can write down:

QH = W + QC

W = QH - QC Rearranging:

Phrased differently, this is just saying that input is equal to output.

Re-expressing the efficiency of a heat engine

Hot reservoir, TH

Cold reservoir, TC

QH

QC

work

= W QH

QC1 - QH

efficiency = QC1 - QH

= W QH

QC

QH

QH - QH

Next we divide through by QH :

= W QCQH -From previous slide:

What does the second law say about heat engine ?

The second law tells us that:Hot reservoir, TH

Cold reservoir, TC

QH

QC

work

ΔSNet ≥ 0

With some algebra, the equation above becomes:

QC1 - QH ≤ TC1 - TH

Using the definition of entropy, we can calculate the net change in entropy of the heat engine during one full cycle:

= ΔSNet QCTH

QH + TC- ≥ 0

The maximum efficiency for a heat engine:

efficiency = QC1 - QH

Recalling that

and putting this together with the result from the previous slide, we get:

Hot reservoir, TH

Cold reservoir, TC

QH

QC

work

efficiency = QC1 -QH

≤ TC1 -TH

2nd Law1st Law

The Carnot Efficiency for a heat engine:

Hot reservoir, TH

Cold reservoir, TC

QH

QC

work

The limit that we have just found, defining that absolute maximum efficiency of a heat engine, is called the Carnot efficiency. To under score this point, NO HEAT ENGINE’S EFFICIENCY CAN EXCEED THE CARNOT EFFICIENCY.

Assumptions that led to the Carnot Efficiency

Hot reservoir, TH

Cold reservoir, TC

QH

QC

work

Conservation of energy

Heat flows from hot to cold

More rigorously:

Hot reservoir, TH

Cold reservoir, TC

QH

QC

work

Conservation of energy (1st law)

2nd Law of Thermodynamics

In what way does the 2nd law of thermodynamics

figure into Asimov’s story.

What are the implications of the second law for the

universe?

What does the Carnot efficiency tell us about the universe? How is

this related to what we were just discussing?

What do you think Asimov is saying with

the ending?

Isaac Asimov’s “The Last Question”• First posed by Alexander Adell and Bertram Lupov on the

occasion during which - “The energy of the Sun was stored, converted, and utilized directly on

a planet-wide scale. All Earth turned off its burning of coal its fissioning uranium, and flipped the switch that connected all of it to a small station, one mile in diameter, circling the Earth at half the distance of the Moon. All Earth ran by invisible beams of sunpower.”

• The question was posed to “Mulitvac”, the most advanced computer. They asked the question, by the way, by typing into a teletype machine. The question was: - Will mankind one day without the net expenditure

of energy be able to restore the Sun to its full youthfulness even after it had died of old age?

- Alternatively, “How can the net amount of entropy of the universe be massively decreased?”

Isaac Asimov’s “The Last Question”• Question is repeated by Jerrodd, who with

his family, is emigrating to the star X-23.

• Question is repeated again by VJ-23 who doesn’t want to submit a pessimistic report to the Galactic Council, once his friend points out that the galaxy will be filled up within five years.

• Again, the question is asked by Zee Prime, some type of ethereal being who’s exact nature is not exactly clarified.

In each case, the answer is roughly: “insufficient data for a meaningful answer”

Isaac Asimov’s “The Last Question”

• In the final few lines of the story, the Cosmic AC, which exists solely in hyperspace, finally says: “Let there be light”, and there was light.

• Is this a religious statement? Is it an actual speculation about our future? Is it just a cheap trick on the part of the author?

Whether or not it is a cheap trick, I would suggest that Asimov is admitting to two facts:

• There are things about the physical universe that we do not understand, such as the Big Bang and many things about black holes.

• It is a fact that we exist, and in a certain sense, we do not know why.

Back to Heat Engines

There are many types of heat engines

• External Combustion Engines. - Cannonball Engine.

- Steam-driven turbines in power plants, where the heat can come from: ‣ Coal ‣ Nuclear ‣ Solar thermal

- Sterling Engines

• Internal Combustion Engines - “Otto Cycle” engines in our cars and trucks.

- “Diesel cycle” engines in our cars and trucks.

- Turbines in jet aircraft, helicopters, tanks, etc.

- Turbines in natural-gas turbine-based power plants.

4-stroke internal combustion engine

1. Intake stroke

2. Compression stroke

3. Power or work

4. Exhauststroke

Stirling Engine

Note that this is CLOSE CYCLE. That is, while heat is absorbed and expelled, the medium (a gas) that expands

and contracts stays within the engine.

Stirling Engine

Solar-thermal technology: one example